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Sep 19, 2013
09/13

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Tohru Eguchi; Kentaro Hori; Chuan-Sheng Xiong

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We propose that the Virasoro algebra controls quantum cohomologies of general Fano manifolds $M$ ($c_1(M)>0$) and determines their partition functions at all genera. We construct Virasoro operators in the case of complex projective spaces and show that they reproduce the results of Kontsevich-Manin, Getzler etc. on the genus-0,1 instanton numbers. We also construct Virasoro operators for a wider class of Fano varieties. The central charge of the algebra is equal to $\chi(M)$, the Euler...

Source: http://arxiv.org/abs/hep-th/9703086v2

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Sep 18, 2013
09/13

by
Kentaro Hori; Cumrun Vafa

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We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type. Standard R -> 1/R duality and dynamical generation of superpotential by vortices are crucial in the derivation. This provides not only a proof of mirror symmetry in the case of (local and global) Calabi-Yau manifolds,...

Source: http://arxiv.org/abs/hep-th/0002222v3

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Jun 29, 2018
06/18

by
Kentaro Hori; Johanna Knapp

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We construct and study a two parameter gauged linear sigma model with gauge group $(U(1)^2\times O(2))/{\mathbb Z}_2$ that has a dual model with gauge group $(U(1)^2\times SO(4))/{\mathbb Z}_2$. The model has two geometric phases, three hybrid phases and one phase whose character is unknown. One of the geometric phases is strongly coupled and the other is weakly coupled, where strong versus weak is exchanged under the duality. They correspond to two Calabi-Yau manifolds with...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1612.06214

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Sep 21, 2013
09/13

by
Jan de Boer; Kentaro Hori; Hirosi Ooguri; Yaron Oz

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The construction of four dimensional supersymmetric gauge theories via the fivebrane of M theory wrapped around a Riemann surface has been successfully applied to the computation of holomorphic quantities of field theory. In this paper we compute non-holomorphic quantities in the eleven dimensional supergravity limit of M theory. While the Kahler potential on the Coulomb of N=2 theories is correctly reproduced, higher derivative terms in the N=2 effective action differ from what is expected for...

Source: http://arxiv.org/abs/hep-th/9711143v1

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Jul 20, 2013
07/13

by
Gary Gibbons; Kentaro Hori; Piljin Yi

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We consider Sen's effective action for unstable D-branes, and study its classical dynamics exactly. In the true vacuum, the Hamiltonian dynamics remains well-defined despite a vanishing action, and is that of massive relativistic string fluid of freely moving electric flux lines. The energy(tension) density equals the flux density in the local co-moving frame. Furthermore, a finite dual Lagrangian exists and is related to the Nielsen-Olesen field theory of ``dual'' strings, supplemented by a...

Source: http://arxiv.org/abs/hep-th/0009061v2

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Jun 30, 2018
06/18

by
Kentaro Hori; Heeyeon Kim; Piljin Yi

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We compute the Witten index of one-dimensional gauged linear sigma models with at least ${\mathcal N}=2$ supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It is subject to a change as the Fayet-Iliopoulos parameter is varied through the phase boundaries. The wall crossing formula is expressed as an integral at infinity of the Coulomb branch. The result is applied to many examples, including quiver quantum...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1407.2567

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Sep 22, 2013
09/13

by
Kentaro Hori

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We study the Type IIA limit of the M theory fivebrane configuration corresponding to N=1 supersymmetric QCD with massless quarks. We identify the effective gauge coupling constant that fits with Novikov-Shifman-Veinshtein-Zakharov exact beta function. We find two different Type IIA limits that correspond to the electric and magnetic descriptions of SQCD, as observed in the massive case by Schmaltz and Sundrum. The analysis is extended to the case of symplectic and orthogonal gauge groups. In...

Source: http://arxiv.org/abs/hep-th/9805142v2

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Sep 23, 2013
09/13

by
Francesco Benini; Richard Eager; Kentaro Hori; Yuji Tachikawa

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We compute the elliptic genera of two-dimensional N=(2,2) and N=(0,2) gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi-Yau, N=(2,2) SU(2) and O(2) gauge theories coupled to N fundamental...

Source: http://arxiv.org/abs/1305.0533v2

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Sep 20, 2013
09/13

by
Kentaro Hori; Johannes Walcher

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We study marginal deformations of B-type D-branes in Landau-Ginzburg orbifolds. The general setup of matrix factorizations allows for exact computations of F-term equations in the low-energy effective theory which are much simpler than in a corresponding geometric description. We present a number of obstructed and unobstructed examples in detail, including one in which a closed string modulus is obstructed by the presence of D-branes. In a certain example, we find a non-trivial global structure...

Source: http://arxiv.org/abs/hep-th/0404196v2

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Sep 17, 2013
09/13

by
Kentaro Hori

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Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ D-branes wrapped on torus fibers to reproduce the mirror duality itself, realizing the program of Strominger-Yau-Zaslow in a slightly different context. Floer theory of intersecting Lagrangians plays an essential role.

Source: http://arxiv.org/abs/hep-th/0207068v1

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Sep 18, 2013
09/13

by
Tohru Eguchi; Kentaro Hori; Chuan-Sheng Xiong

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We discuss how the theory of quantum cohomology may be generalized to ``gravitational quantum cohomology'' by studying topological sigma models coupled to two-dimensional gravity. We first consider sigma models defined on a general Fano manifold $M$ (manifold with a positive first Chern class) and derive new recursion relations for its two point functions. We then derive bi-Hamiltonian structures of the theories and show that they are completely integrable at least at the level of genus $0$. We...

Source: http://arxiv.org/abs/hep-th/9605225v1

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Jul 20, 2013
07/13

by
Kentaro Hori

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We show that the transformation of D-branes under T-duality on four-torus is represented by Nahm transform of instantons. The argument for this allows us to generalize Nahm transform to the case of orthogonal and symplectic gauge groups as well as to instantons on Z_2 orbifold of four-torus. In addition, we identify the isomorphism of K-theory groups that realizes the transformation of D-brane charges under T-duality on torus of arbitrary dimensions. By the isomorphism we are lead to identify...

Source: http://arxiv.org/abs/hep-th/9902102v2

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Sep 21, 2013
09/13

by
Kentaro Hori

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We study the low energy behaviour of N=(2,2) supersymmetric gauge theories in 1+1 dimensions, with orthogonal and symplectic gauge groups and matters in the fundamental representation. We observe supersymmetry breaking in super-Yang-Mills theory and in theories with small numbers of flavors. For larger numbers of flavors, we discover duality between regular theories with different gauge groups and matter contents, where regularity refers to absence of quantum Coulomb branch. The result is...

Source: http://arxiv.org/abs/1104.2853v2

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Sep 21, 2013
09/13

by
Kentaro Hori; Hirosi Ooguri; Cumrun Vafa

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We show how Higgs mechanism for non-abelian N=2 gauge theories in four dimensions is geometrically realized in the context of type II strings as transitions among compactifications of Calabi-Yau threefolds. We use this result and T-duality of a further compacitification on a circle to derive N=4, d=3 dual field theories. This reduces dualities for N=4 gauge systems in three dimensions to perturbative symmetries of string theory. Moreover we find that the dual of a gauge system always exists but...

Source: http://arxiv.org/abs/hep-th/9705220v1

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Sep 19, 2013
09/13

by
Ilka Brunner; Kentaro Hori

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We review and develop the construction of crosscap states associated with parity symmetries in rational conformal field theories. A general method to construct crosscap states in abelian orbifold models is presented. It is then applied to rational U(1) and parafermion systems, where in addition we study the geometrical interpretation of the corresponding parities.

Source: http://arxiv.org/abs/hep-th/0208141v1

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Sep 23, 2013
09/13

by
Tohru Eguchi; Kentaro Hori

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Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. In the case of SCFTs constructed from pure gauge theories without matter $N=2$ critical points seem to be classified according to the A-D-E classification as in the two-dimensional SCFTs.

Source: http://arxiv.org/abs/hep-th/9607125v1

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Sep 19, 2013
09/13

by
Jan de Boer; Kentaro Hori; Yaron Oz

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We study the structure of the moduli spaces of vacua and superpotentials of N=2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N=2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with...

Source: http://arxiv.org/abs/hep-th/9703100v3

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Sep 22, 2013
09/13

by
Kentaro Hori

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We derive some consistency conditions for fivebrane in M theory on R^5/Z_2 orbifold from the quantization law for the antisymmetric tensor field. We construct consistent fivebrane configurations in R^5/Z_2 type orbifold that exhibit the correct low energy dynamics of N=2 SQCD in four dimensions with symplectic and orthogonal gauge groups. This leads us to propose the M theory realization of orientifold four-planes of various types, and we study their properties by applying the consistency...

Source: http://arxiv.org/abs/hep-th/9805141v2

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Sep 22, 2013
09/13

by
Jan de Boer; Kentaro Hori; Hirosi Ooguri; Yaron Oz; Zheng Yin

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We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N=4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL(2,Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane worldvolume theory via...

Source: http://arxiv.org/abs/hep-th/9612131v1

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Sep 21, 2013
09/13

by
Kentaro Hori; Anton Kapustin

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We provide a world-sheet description of Neveu-Schwarz five-branes wrapped on a complex projective space. It is an orbifold of the product of an N=2 minimal model and the IR fixed point of a certain linear sigma model. We show how the naked singularity in the supergravity description is resolved by the world-sheet CFT. Applying mirror symmetry, we show that the low-energy theory of NS5-branes wrapped on CP^1 in Eguchi-Hanson space is described by the Seiberg-Witten prepotential for N=2...

Source: http://arxiv.org/abs/hep-th/0203147v1

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Sep 18, 2013
09/13

by
Oren Bergman; Kentaro Hori; Piljin Yi

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A non-perturbative confinement mechanism has been proposed to explain the fate of the unbroken gauge group on the world-volume of annihilating D-brane-anti-D-brane pairs. In this paper, we examine this phenomenon closely from several different perspectives. Existence of the confinement mechanism is most easily seen by noticing that the fundamental string emerges as the confined electric flux string at the end of the annihilation process. After reviewing the confinement proposal in general, this...

Source: http://arxiv.org/abs/hep-th/0002223v2

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Sep 20, 2013
09/13

by
Kentaro Hori

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This is a thesis for Rigaku-Hakushi($\simeq$ Ph. D.). It clarifies the geometric meaning and field theoretical consequences of the spectral flows acting on the space of states of the `$G/H$ coset model'. As suggested by Moore and Seiberg, the spectral flow is realized as the response of states to certain change of background gauge field together with the gauge transformation on a circle. Applied to the boundary circle of a disc with field insertion, such a realization leads to a certain...

Source: http://arxiv.org/abs/hep-th/9402019v1

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Sep 20, 2013
09/13

by
Jan de Boer; Kentaro Hori; Hirosi Ooguri

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We study membrane scattering in a curved space with non-zero M-momentum p_{11} transfer. In the low-energy short-distance region, the membrane dynamics is described by a three-dimensional N=4 supersymmetric gauge theory. We study an n-instanton process of the gauge theory, corresponding to the exchange of n units of p_{11}, and compare the result with the scattering amplitude computed in the low-energy long-distance region using supergravity. We find that they behave differently. We show that...

Source: http://arxiv.org/abs/hep-th/9802005v1

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Jul 20, 2013
07/13

by
Kentaro Hori; David Tong

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We study various aspects of N=(2,2) supersymmetric non-Abelian gauge theories in two dimensions, with applications to string vacua. We compute the Witten index of SU(k) SQCD with N>0 flavors with twisted masses; the result is presented as the solution to a simple combinatoric problem. We further claim that the infra-red fixed point of SU(k) gauge theory with N massless flavors is non-singular if (k,N) passes a related combinatoric criterion. These results are applied to the study of a class...

Source: http://arxiv.org/abs/hep-th/0609032v2

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Jul 20, 2013
07/13

by
Kentaro Hori

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A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with quasi-parabolic structure. Two actions of the fundamental group of the gauge group is defined: One on the space of gauge invariant local fields and the other on the moduli spaces. Applying these in the integral expression, we obtain a certain identity which...

Source: http://arxiv.org/abs/hep-th/9411134v1

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Sep 18, 2013
09/13

by
Kentaro Hori; Johannes Walcher

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We construct and classify categories of D-branes in orientifolds based on Landau-Ginzburg models and their orbifolds. Consistency of the worldsheet parity action on the matrix factorizations plays the key role. This provides all the requisite data for an orientifold construction after embedding in string theory. One of our main results is a computation of topological field theory correlators on unoriented worldsheets, generalizing the formulas of Vafa and Kapustin-Li for oriented worldsheets,...

Source: http://arxiv.org/abs/hep-th/0606179v1

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Sep 20, 2013
09/13

by
Tohru Eguchi; Kentaro Hori; Katsushi Ito; Sung-Kil Yang

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Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have constructed represent universality classes of the 4-dimensional $N=2$ SCFTs.

Source: http://arxiv.org/abs/hep-th/9603002v1

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Jul 20, 2013
07/13

by
Kentaro Hori

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New relations of correlation functions are found in topological string theory; one for each second cohomology class of the target space. They are close cousins of the Deligne-Dijkgraaf-Witten's puncture and dilaton equations. When combined with the dilaton equation and the ghost number conservation, the equation for the first chern class of the target space gives a constraint on the topological sum (over genera and (multi-)degrees) of partition functions. For the $\CP^1$ model, it coincides...

Source: http://arxiv.org/abs/hep-th/9411135v2

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Sep 19, 2013
09/13

by
Jan de Boer; Kentaro Hori; Hirosi Ooguri; Yaron Oz

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We study dynamical supersymmetry breaking in four dimensions using the fivebrane of M theory, in particular for the Izawa-Yanagida-Intriligator-Thomas (IYIT) model, which we realize as the worldvolume theory of a certain M-theory fivebrane configuration. From the brane point of view, supersymmetry is broken when a holomorphic configuration with the proper boundary conditions does not exist. We discuss the difference between explicit and spontaneous supersymmetry breaking and between runaway...

Source: http://arxiv.org/abs/hep-th/9801060v2

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Sep 22, 2013
09/13

by
Dongfeng Gao; Kentaro Hori

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We determine the structure of the Chan-Paton factors of the open strings ending on space filling D-branes in Type II orientifolds. Through the analysis, we obtain a rule concerning possible distribution of O-plane types. The result is applied to classify the topology of D-branes in terms of Fredholm operators and K-theory, deriving a proposal made earlier and extending it to more general cases. It is also applied to compactifications with N=1 supersymmetry in four-dimensions. We adapt and...

Source: http://arxiv.org/abs/1004.3972v1

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Sep 22, 2013
09/13

by
Amihay Hanany; Kentaro Hori

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Type IIA brane configurations are used to construct N=2 supersymmetric gauge theories in two dimensions. Using localization of chiral multiplets in ten-dimensional spacetime, supersymmetric non-linear sigma models with target space such as $\CP^{n-1}$ and the Grassmann manifolds are studied in detail. The quantum properties of these models are realized in $M$ theory by taking the strong Type IIA coupling limit. The brane picture implies an equivalence between the parameter space of N=2...

Source: http://arxiv.org/abs/hep-th/9707192v2

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Sep 20, 2013
09/13

by
Jan de Boer; Kentaro Hori; Hirosi Ooguri; Yaron Oz

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We construct and analyze dual N=4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters. We analyze the classical and the quantum moduli spaces of the theories and construct an explicit mirror map between the mass parameters and the the Fayet-Iliopoulos parameters of the...

Source: http://arxiv.org/abs/hep-th/9611063v2

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Jul 20, 2013
07/13

by
Jan de Boer; Kentaro Hori; Yaron Oz; Zheng Yin

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We use brane configurations and SL(2,Z) symmetry of the type IIB string to construct mirror N=2 supersymmetric gauge theories in three dimensions. The mirror map exchanges Higgs and Coulomb branches, Fayet-Iliopoulos and mass parameters and U(1)R symmetries. Some quantities that are determined at the quantum level in one theory are determined at the classical level of the mirror. One such example is the complex structure of the Coulomb branch of one theory which is determined quantum...

Source: http://arxiv.org/abs/hep-th/9702154v1

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Sep 22, 2013
09/13

by
Kentaro Hori; Johannes Walcher

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B-type D-branes can be obtained from matrix factorizations of the Landau-Ginzburg superpotential. We here review this promising approach to learning about the spacetime superpotential of Calabi-Yau compactifications. We discuss the grading of the D-branes, and present applications in two examples: the two-dimensional torus, and the quintic.

Source: http://arxiv.org/abs/hep-th/0409204v1

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Sep 18, 2013
09/13

by
Manfred Herbst; Kentaro Hori; David Page

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We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton factor, which can be used to define a family of D-branes over a region of the K\"ahler moduli space that connects special points of different character. As an application, we find a precise, transparent relation between D-branes in various geometric phases as well as free orbifold and...

Source: http://arxiv.org/abs/0803.2045v1

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Sep 18, 2013
09/13

by
Mina Aganagic; Kentaro Hori; Andreas Karch; David Tong

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We study the Coulomb-Higgs duality of N=2 supersymmetric Abelian Chern-Simons theories in 2+1 dimensions, by compactifying dual pairs on a circle of radius R and comparing the resulting N=(2,2) theories in 1+1 dimensions. Below the compactification scale, the theory on the Higgs branch reduces to the non-linear sigma model on a toric manifold. In the dual theory on the Coulomb branch, the Kaluza-Klein modes generate an infinite tower of contributions to the superpotential. After resummation, in...

Source: http://arxiv.org/abs/hep-th/0105075v1

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Sep 18, 2013
09/13

by
Bobby Acharya; Mina Aganagic; Kentaro Hori; Cumrun Vafa

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We consider orientifolds of Calabi-Yau 3-folds in the context of Type IIA and Type IIB superstrings. We show how mirror symmetry can be used to sum up worldsheet instanton contributions to the superpotential for Type IIA superstrings. The relevant worldsheets have the topology of the disc and ${\bf RP^2}$.

Source: http://arxiv.org/abs/hep-th/0202208v1

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Sep 20, 2013
09/13

by
Kentaro Hori; Kazuo Hosomichi; David C. Page; Raul Rabadan; Johannes Walcher

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After orientifold projection, the conifold singularity in hypermultiplet moduli space of Calabi-Yau compactifications cannot be avoided by geometric deformations. We study the non-perturbative fate of this singularity in a local model involving O6-planes and D6-branes wrapping the deformed conifold in Type IIA string theory. We classify possible A-type orientifolds of the deformed conifold and find that they cannot all be continued to the small resolution. When passing through the singularity...

Source: http://arxiv.org/abs/hep-th/0506234v2

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Sep 24, 2013
09/13

by
Jan de Boer; Robbert Dijkgraaf; Kentaro Hori; Arjan Keurentjes; John Morgan; David R. Morrison; Savdeep Sethi

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We study string compactifications with sixteen supersymmetries. The moduli space for these compactifications becomes quite intricate in lower dimensions, partly because there are many different irreducible components. We focus primarily, but not exclusively, on compactifications to seven or more dimensions. These vacua can be realized in a number ways: the perturbative constructions we study include toroidal compactifications of the heterotic/type I strings, asymmetric orbifolds, and...

Source: http://arxiv.org/abs/hep-th/0103170v3

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Jul 22, 2013
07/13

by
Kentaro Hori; Yaron Oz

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We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane R-R charge and a 0-brane R-R charge. We study the action of the T-duality on the moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We apply the construction to F-theory compactified on a Calabi-Yau 4-fold and study the duality of N=2 SU(N_c) gauge theories in four dimensions. We discuss the generalization to the N=1 duality scenario.

Source: http://arxiv.org/abs/hep-th/9702173v2

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Sep 18, 2013
09/13

by
Kentaro Hori

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We construct a class of supersymmetric boundary interactions in N=2 field theories on the half-space, which depend on parameters that are not at all renormalized or not renormalized in perturbation theory beyond one-loop. This can be used to study D-branes wrapped on a certain class of Lagrangian submanifolds as well as holomorphic cycles. The construction of holomorphic D-branes is in close relationship with the background independent open string field theory approach to brane/anti-brane...

Source: http://arxiv.org/abs/hep-th/0012179v1

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Sep 22, 2013
09/13

by
Kentaro Hori

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We report on recent progress in understanding mirror symmetry. Some of more recent generalizations and applications are also presented. --- A contribution to the Proceedings of ``Strings 2001'' at Mumbai, India.

Source: http://arxiv.org/abs/hep-th/0106043v2

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Sep 18, 2013
09/13

by
Ilka Brunner; Kentaro Hori

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We study parity symmetries and crosscap states in classes of N=2 supersymmetric quantum field theories in 1+1 dimensions, including non-linear sigma models, gauged WZW models, Landau-Ginzburg models, and linear sigma models. The parity anomaly and its cancellation play important roles in many of them. The case of the N=2 minimal model are studied in complete detail, from all three realizations -- gauged WZW model, abstract RCFT, and LG models. We also identify mirror pairs of orientifolds,...

Source: http://arxiv.org/abs/hep-th/0303135v2

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Sep 18, 2013
09/13

by
Kentaro Hori; Amer Iqbal; Cumrun Vafa

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We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulk supercharges in non-linear sigma models, gauged linear sigma models, and Landau-Ginzburg models. We identify a mechanism for brane creation in LG theories and provide a new derivation of a link between soliton numbers of the massive theories and R-charges of vacua at the UV fixed point. Moreover we...

Source: http://arxiv.org/abs/hep-th/0005247v2

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Sep 18, 2013
09/13

by
Ilka Brunner; Kentaro Hori; Kazuo Hosomichi; Johannes Walcher

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We systematically construct and study Type II Orientifolds based on Gepner models which have N=1 supersymmetry in 3+1 dimensions. We classify the parity symmetries and construct the crosscap states. We write down the conditions that a configuration of rational branes must satisfy for consistency (tadpole cancellation and rank constraints) and spacetime supersymmetry. For certain cases, including Type IIB orientifolds of the quintic and a two parameter model, one can find all solutions in this...

Source: http://arxiv.org/abs/hep-th/0401137v1

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Sep 18, 2013
09/13

by
Kentaro Hori

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We study boundary renormalization group flows of N=2 minimal models using Landau-Ginzburg description of B-type. A simple algebraic relation of matrices is relevant. We determine the pattern of the flows and identify the operators that generate them. As an application, we show that the charge lattice of B-branes in the level k minimal model is Z_{k+2}. We also reproduce the fact that the charge lattice for the A-branes is Z^{k+1}, applying the B-brane analysis on the mirror LG orbifold.

Source: http://arxiv.org/abs/hep-th/0401139v1

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Sep 21, 2013
09/13

by
Kentaro Hori; Anton Kapustin

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We prove the equivalence of the SL(2,R)/U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N=2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the charged scalar fields and taking into account the vortex-instanton effects, as proposed recently in...

Source: http://arxiv.org/abs/hep-th/0104202v2